Typical entanglement in multiple-qubit systems

Vivien Kendon, Kae Nemoto, William Munro

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Quantum entanglement and its paradoxical properties hold the key to an information processing revolution. Much attention has focused recently on the challenging problem of characterizing entanglement. Entanglement for a two qubit system is reasonably well understood; however, the nature and properties of multiple qubit systems are largely unexplored. Motivated by the importance of such systems in quantum computing, we show that typical pure states of N qubits are highly entangled but have decreasing amounts of pairwise entanglement (measured using the Wootter concurrence formula) as N increases. Above six qubits, very few states have any pairwise entanglement and, generally, for a typical pure state of N qubits there is a sharp cut-off where its subsystems of size m become positive partial transpose (i.e. separable or only bound entangled) around N ≳ 2m + 3, based on numerical analysis up to N = 13.
Original languageEnglish
Pages (from-to)1709-1716
Number of pages8
JournalJournal of Modern Optics
Issue number10
Publication statusPublished - 31 Dec 2002


  • computational methods
  • numerical methods
  • optical data processing
  • optical properties
  • optical variables measurement
  • multiple qubit systems
  • quantum computing
  • quantum entanglement
  • Wootter concurrence formula
  • quantum optics


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